Magnetic Resonance Imaging (MRI) or Nuclear Magnetic Resonance (NMR) imaging generally provides spatial discrimination of resonant interactions between radio frequency (RF) waves on nuclei in a magnetic field. Specifically, MRI utilizes hydrogen nuclear spins of the water molecules in the human body, which are polarized by a strong, uniform, static magnetic field, commonly referred to as B0 or the main magnetic field. When a substance, such as human tissue, is subjected to the main magnetic field, the individual magnetic moments of the spins in the tissue attempt to align with the main magnetic field. When excited by an RF wave, the spins precess about the main magnetic field at a characteristic Larmor frequency. Signals are emitted by the excited spins, which are processed to generate Magnetic Resonance (MR) images of the subject.
Electrical properties of substances, such as human tissue, exposed to MRI can provide insight into a response of the substances to such imaging. For example, a determination of the electrical properties of tissue including conductivity and permittivity are useful in estimating local RF power deposition (also known as local specific absorption rate or SAR) during acquisition of MR images. The electrical properties of tissue can also be useful in discriminating between malignant and healthy tissue (e.g., malignant tissue has been shown to have higher permittivity and conductivity than surrounding healthy tissue). The electrical properties of tissue are also required for treatment planning of therapeutic applications of heat using radio frequency, e.g., RF hyperthermia.
Determining the electrical properties of tissue in-vivo using MRI has posed several problems due to the inability to directly measure the phase of the receive RF magnetic field B1− and the phase of the transmit RF magnetic field B1+. To overcome this limitation, conventional approaches using MRI have estimated the electrical properties of tissue using the transmit RF magnetic field B1+, for example, by mapping the amplitude of the transmit RF magnetic field and approximating the phase of the transmit magnetic field. Conventional MR-based electrical property measurement techniques typically rely on mapping the transmit RF field B1+, by attempting to eliminate the effect of the receive RF field B1− from the MR images used for the measurements. The amplitude of B1+ can be obtained using various approaches, such as Bloch-Siegert B1+ mapping or the double-angle method. The phase of B1+, on the other hand, is generally more difficult to separate from the phase of B1−. Methods have been proposed to approximate the phase of B1+. Using conventional methods, a complex map of B1+ is formed and the map is subjected to Laplacian operation to produce k2 (complex wave vector) maps and subsequently electrical properties maps.
While conventional approaches have provided techniques for estimating the electrical properties of tissue based on mapping the amplitude of B1+ and approximating the phase of B1+, implementations of conventional approaches to generating electrical properties maps are vulnerable to poor results due to noise in B1+ data. This has been addressed by using larger regions to calculate Laplacian operation (e.g. skip factors which consider data points far apart, resulting in differences that are larger than noise terms, increasing the overall SNR of the calculation)
Typically, the use of such skip factors requires a larger area for the estimation of the Laplacian at each pixel location, which can reduce the resolution of the images corresponding to the electrical properties. In other approaches, non-physical values (e.g. negative conductivity) resulting from noise in B1 data have been discarded. The missing pixels were replaced by average values in a local region. In yet other efforts, smoothing of B1+ data have been carried out to remove noise. These approaches can lead to lower resolution or inaccurate results.